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Superforms in Simple Six-dimensional Superspace

We investigate the complex of differential forms in curved, six-dimensional, $N=(1,0)$ superspace. The superconformal group acts on this complex by super-Weyl transformations. An ambi-twistor-like representation of a second conformal group arises on a pure spinor subspace of the cotangent space. The $p$-forms are defined by super-Weyl-covariant tensor fields on this pure spinor subspace. The on-shell dynamics of such fields is superconformal. We construct the superspace de Rham complex by successively obstructing the closure of forms. We then extend the analysis to composite forms obtained by wedging together forms of lower degree Finally, we comment on applications to integration in curved superspace and give a superspace formulation of the abelian limit of the non-abelian tensor hierarchy of $N=(1,0)$ superconformal models and propose a formulation of it as a Chern-Simons theory on the ambi-twistor-like superspace.